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Re: Help with Matrix math!

by rg0now (Chaplain)
on Dec 17, 2007 at 19:04 UTC ( #657486=note: print w/replies, xml ) Need Help??

in reply to Help with Matrix math!

What you are trying to solve is a nonlinearly constrained nonlinear (actually, quadratic) mathematical program. This is a tough one, I can tell you...

However, all is not lost, because you might be able to simplify your problem into something actually soluble.

First: are you absolutely sure that you want to optimize over the boundary of the unit ball (this is what the constraint x'x=1 seems to impose)? Isn't it enough to only assure that x is constrained into a sane region, like e.g., the n-dimensional unit box? If it is, you get a quadratic program:

max_x (x' D x) s.t. -1 <= x_i <= 1 \forall i=1..n
See more on quadratic programs here: Quadratic programming.

Second: all depends on whether or not your D is negative definite or not (all eigenvalues are negative). If not, you are out of luck: the problem is (at least) NP hard. If, on the other hand, D is nicely negative definite, then the objective function is concave and the uniqueness of the optimal solution is guaranteed. In this case, you could use a commercial quadratic solver, like CPLEX, or, after suitable linearization, a linear program solver. too. E.g., this one Math::GLPK has a nice Perl interface (believe me it's nice: I wrote it!...:-).

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Corion idly wonders about creating a series of HTTP requests. There seems to be no framework to generate a series of HTTP requests, like "try all these requests"
[Corion]: This is vaguely inspired by that list of "nasty" strings, which I'd like to replace among HTTP parameters, just to see whether the application crashes, but also for easy downloading of a list of URLs etc
[Corion]: Maybe I'll just conoct something using Algorithm::Permute to create an (OO) generator for such requests, or a simple function.
[Corion]: For testing I imagine one would want to test a random sampling of such "bad"/"unexpected" requests, while for downloading, one would want to generate them all in order, but not necessarily as a huge list

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